Merger rates of dark matter haloes: a comparison between EPS and N-body results

TL;DR

This study compares analytical EPS models with N-body simulation results for dark matter halo merger rates across various masses and redshifts, highlighting the models' varying accuracy depending on specific conditions.

Contribution

It provides a detailed comparison of spherical and ellipsoidal EPS models with N-body simulations, identifying their strengths and limitations in predicting halo merger rates.

Findings

Agreement varies with halo mass and redshift.

Neither model consistently matches N-body results across all parameters.

Discrepancies depend on the progenitor distribution and EPS method used.

Abstract

We calculate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3 and they have been compared with merger rates that have been proposed by other authors as fits to the results of N-body simulations. The detailed comparison presented here shows that the agreement between the analytical models and N-body simulations depends crucially on the mass of the descendant halo. For some range of masses and redshifts either SC or EC models approximate satisfactory the results of N-body simulations but for other cases both models are less satisfactory or even bad approximations. We showed, by studying the parameters of the problem that a disagreement --if it appears-- does not depend on the values of the parameters but on the kind of the particular solution used for the distribution of progenitors or on the nature of EPS methods. Further studies could help to improve our understanding about the physical processes during the formation of dark matter haloes.